If I’m not mistaken, such problems would contain some enumerated hypotheses—point peaks in a well-defined parameter space—and the NOTA hypothesis would be a uniformly thin layer over the rest of that space. Can’t tell what key features the data-generating process must have, though. Or am I failing reading comprehension again?
If I’m not mistaken, such problems would contain some enumerated hypotheses—point peaks in a well-defined parameter space—and the NOTA hypothesis would be a uniformly thin layer over the rest of that space
Yep.
Can’t tell what key features the data-generating process must have, though.
I think the key features that make the NOTA hypothesis feasible are (i) all possible hypotheses generate signals of a known form (but with free parameters), and (ii) although the space of all possible hypotheses is too large to enumerate, we have a partial library of “interesting” hypotheses of particularly high prior probability for which the generated signals are known even more specifically than in the general case.
If I’m not mistaken, such problems would contain some enumerated hypotheses—point peaks in a well-defined parameter space—and the NOTA hypothesis would be a uniformly thin layer over the rest of that space. Can’t tell what key features the data-generating process must have, though. Or am I failing reading comprehension again?
Yep.
I think the key features that make the NOTA hypothesis feasible are (i) all possible hypotheses generate signals of a known form (but with free parameters), and (ii) although the space of all possible hypotheses is too large to enumerate, we have a partial library of “interesting” hypotheses of particularly high prior probability for which the generated signals are known even more specifically than in the general case.